2019 AIME II Problems/Problem 8
Problem 8
The polynomial has real coefficients not exceeding , and . Find the remainder when is divided by .
Solution
We have where is a primitive 6th root of unity. Then we have
We wish to find . We first look at the real parts. As and , we have . Looking at imaginary parts, we have , so . As and do not exceed 2019, we must have . Then , so .
-scrabbler94
See Also
2019 AIME II (Problems • Answer Key • Resources) | ||
Preceded by Problem 7 |
Followed by Problem 9 | |
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